Clearance (pharmacology)
In pharmacology, clearance is a pharmacokinetic measurement of the volume of plasma from which a substance is completely removed per unit time. Usually, clearance is measured in L/h or mL/min. The quantity reflects the rate of drug elimination divided by plasma concentration. Excretion, on the other hand, is a measurement of the amount of a substance removed from the body per unit time. While clearance and excretion of a substance are related, they are not the same thing. The concept of clearance was described by Thomas Addis, a graduate of the University of Edinburgh Medical School.
Substances in the body can be cleared by various organs, including the kidneys, liver, lungs, etc. Thus, total body clearance is equal to the sum clearance of the substance by each organ glomerular filtration, 2) secretion from the peritubular capillaries to the nephron, and 3) reabsorption from the nephron back to the peritubular capillaries. Clearance is variable in zero-order kinetics because a constant amount of the drug is eliminated per unit time, but it is constant in first-order kinetics, because the amount of drug eliminated per unit time changes with the concentration of drug in the blood.
Clearance can refer to the volume of plasma from which the substance is removed per unit time or, in some cases, inter-compartmental clearances can be discussed when referring to redistribution between body compartments such as plasma, muscle, and fat.
Definition
When referring to the function of the kidney, clearance is considered to be the amount of liquid filtered out of the blood that gets processed by the kidneys or the amount of blood cleaned per time because it has the units of a volumetric flow rate . However, it does not refer to a real value; "the kidney does not completely remove a substance from the total renal plasma flow." From a mass transfer perspective and physiologically, volumetric blood flow is only one of several factors that determine blood concentration and removal of a substance from the body. Other factors include the mass transfer coefficient, dialysate flow and dialysate recirculation flow for hemodialysis, and the glomerular filtration rate and the tubular reabsorption rate, for the kidney. A physiologic interpretation of clearance is that clearance is a ratio of the mass generation and blood concentration.Its definition follows from the differential equation that describes exponential decay and is used to model kidney function and hemodialysis machine function:
Where:
- is the mass generation rate of the substance - assumed to be a constant, i.e. not a function of time or
- t is dialysis time or time since injection of the substance/drug or
- V is the volume of distribution or total body water or
- K is the clearance or
- C is the concentration or
It is derived from a mass balance.
Clearance of a substance is sometimes expressed as the inverse of the time constant that describes its removal rate from the body divided by its volume of distribution.
In steady-state, it is defined as the mass generation rate of a substance divided by its concentration in the blood.
Clearance, half-life and distribution volume
There is an important relationship between clearance, elimination half-life and distribution volume.
The elimination rate constant of a drug Κel is equivalent to total clearance divided by the distribution volume. But Κel is also equivalent to ln2 divided by elimination rate half-life t1/2. Thus, Cltot = ln2 Vd/t1/2. This means, for example, that an increase in total clearance results in a decrease in elimination rate half-life, provided distribution volume is constant. Derivation of these equations can be found in e.g. Rang and Dale's Pharmacology
Effect of plasma protein binding
For substances that exhibit substantial plasma protein binding, clearance is generally dependent on the total concentration and not the free concentration.Most plasma substances have primarily their free concentrations regulated, which thus remains the same, so extensive protein binding increases total plasma concentration. This decreases clearance compared to what would have been the case if the substance did not bind to protein. However, the mass removal rate is the same, because it depends only on concentration of free substance, and is independent on plasma protein binding, even with the fact that plasma proteins increase in concentration in the distal renal glomerulus as plasma is filtered into Bowman's capsule, because the relative increases in concentrations of substance-protein and non-occupied protein are equal and therefore give no net binding or dissociation of substances from plasma proteins, thus giving a constant plasma concentration of free substance throughout the glomerulus, which also would have been the case without any plasma protein binding.
In other sites than the kidneys, however, where clearance is made by membrane transport proteins rather than filtration, extensive plasma protein binding may increase clearance by keeping concentration of free substance fairly constant throughout the capillary bed, inhibiting a decrease in clearance caused by decreased concentration of free substance through the capillary.
Derivation of equation
Equation 1 is derived from a mass balance:where:
- is a period of time
- the change in mass of the toxin in the body during
- is the toxin intake rate
- is the toxin removal rate
- is the toxin generation rate
Since
and
Equation A1 can be rewritten as:
If one lumps the in and gen. terms together, i.e. and divides by the result is a difference equation:
If one applies the limit one obtains a differential equation:
Using the Product Rule this can be rewritten as:
If one assumes that the volume change is not significant, i.e., the result is Equation 1:
Solution to the differential equation
The general solution of the above differential equation is:Where:
- Co is the concentration at the beginning of dialysis or the initial concentration of the substance/drug or
- e is the base of the natural logarithm
Steady-state solution
The above equation can be rewritten as:
The above equation makes clear the relationship between mass removal and clearance. It states that the concentration and clearance vary inversely with one another. If applied to creatinine, it follows from the equation that if the serum creatinine doubles the clearance halves and that if the serum creatinine quadruples the clearance is quartered.
Measurement of renal clearance
Renal clearance can be measured with a timed collection of urine and an analysis of its composition with the aid of the following equation :Where:
- K is the clearance
- CU is the urine concentration
- Q is the urine flow
- CB is the plasma concentration
Note - the above equation is valid only for the steady-state condition. If the substance being cleared is not at a constant plasma concentration K must be obtained from the solution of the differential equation.